Solve the given equation for x. 3^5x-6=36 x=square

To solve the equation $3^{5x-6}=36$, we can take the logarithm of both sides of the equation to get:<br /><br />$\log(3^{5x-6})=\log(36)$<br /><br />Using the property of logarithms that $\log(a^b)=b\log(a)$, we can rewrite the left side of the equation as:<br /><br />$(5x-6)\log(3)=\log(36)$<br /><br />Now, we can solve for $x$ by isolating it on one side of the equation:<br /><br />$5x-6=\frac{\log(36)}{\log(3)}$<br /><br />$5x=\frac{\log(36)}{\log(3)}+6$<br /><br />$x=\frac{1}{5}\left(\frac{\log(36)}{\log(3)}+6\right)$<br /><br />Therefore, the solution to the equation $3^{5x-6}=36$ is $x=\frac{1}{5}\left(\frac{\log(36)}{\log(3)}+6\right)$.